It is often useful to generate a list of all the CMYK formulations that can be used to make a specified color, and then choose a formulation from the list to satisfy other considerations. Existing ways of doing this are quite slow, so, for example, finding all the formulations for all the nodes of a 33×33×33 LAB to CMYK rendering lookup table (LUT) involving 35,937 nodes would take too long. Therefore, previous techniques for generating such LUTs require the user to specify a GCR to limit the number of CMYK formulations that need be considered. Simple heuristics are often used to determine this GCR, and this often leads to sub-optimal results. The availability of a way to quickly generate CMYK formulation lists also enables the optimal solution of several other color management problems. What is needed are methods for efficiently searching for the locus in a manner which does not depend on an analytic expression but rather relies upon the geometry of the CMYK to LAB multi-dimensional LUT usually used to describe the response of the printer (the printer model) so as to quickly generate CMYK formulations.
Accordingly, what is needed are increasingly sophisticated systems and methods for determining a locus of colorant formulations that produce a desired color on a four colorant marking device which can help effectuate an optimal solution for color management problems.